# Completing the square quadratic formula

## Completing the square But if you have time, let me show you how to "Complete the Square" yourself. We can complete the square to solve a Quadratic Equation (find where it is equal .

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If you're seeing this message, it means we're having trouble loading external resources on our website. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Solving quadratics by completing the square. Worked example: Completing the square intro. Practice: Completing the square intro.

The Process The Formula. Some quadratics are fairly simple to solve because they are of the form "something-with- x squared equals some number", and then you take the square root of both sides. Completing the Square. Unfortunately, most quadratics don't come neatly squared like this. For your average everyday quadratic, you first have to use the technique of "completing the square" to rearrange the quadratic into the neat " squared part equals a number " format demonstrated above. For example:. Now, let's start the completing-the-square process.

The Quadratic Formula. Learning Objective s. You can solve any quadratic equation by completing the square —rewriting part of the equation as a perfect square trinomial. This equation is known as the Quadratic Formula. This formula is very helpful for solving quadratic equations that are difficult or impossible to factor, and using it can be faster than completing the square. Standard Form.

Proof of the quadratic formula. We will now see how to apply it to solving a quadratic equation. In Lesson 18 there are examples and problems in which the coefficient of x is odd. Also, some of the quadratics below have complex roots, and some involve simplifying radicals. Problem 6. Solve each quadratic equation by completing the square.

The Process The Formula. To complete this exercise, I'll apply the same procedure as was demonstrated on the previous page. Then I'll rearrange this equation to get the variable-containing terms on the left-hand side, with the constant the loose number isolated on the right-hand side:. The Quadratic Formula. The leading term is multiplied by an "understood" 1 , so I don't have to divide through by anything.

## Completing the Square: Deriving the Quadratic Formula

But if you have time, let me show you how to " Complete the Square " yourself. Having x twice in the same expression can make life hard.

## Lesson 37, Quadratic equations: Section 2

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